Ever since Michael Behe published Darwin’s Black Box in 1996, the concept of irreducible complexity has played a central role in the debate over Darwinian theory. I am proposing a new, theoretical method of determining whether a system is irreducibly complex using power-sets. First, however, it is necessary to define irreducible complexity.
Various definitions of irreducible complexity exist. Michael Behe defines it as “a single system which is composed of several interacting parts, and where the removal of any one of the parts causes the system to cease functioning.” Critics have noted that this definition is actually a definition of interlocking complexity, a concept H. J. Muller had written about years earlier and which is perfectly compatible with Darwinian theory. In this article, I will be using the definition provided by Charles Darwin himself. Although the term did not exist in Darwin’s day, the concept was foreseen; it was, moreover, readily acknowledged that any example of an irreducibly complex system would break down Darwinian theory. According to Darwin: “If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down.” In the following paragraph, he follows this by warning, “We should be extremely cautious in concluding that an organ could not have been formed by transitional gradations of some kind.” It would, indeed, be ridiculous to rule out evolutionary explanations simply because we don’t know how they evolved; these explanations may be put in doubt, but they could not be ruled out absolutely. Thus, in the scientific search for irreducible complexity it is imperative that scientists be meticulous in considering every possible slight modification. It is only if all possibilities for a given evolutionary gradation would break down the system, either being physically impossible without the other parts, or otherwise harmful to the organism, that it can be said with certainty that the system in question is irreducibly complex and could not, therefore, have been the result of evolution alone.
I am proposing power-sets as a method which may be used to approach the issue. The veracity of this approach, however, must be tested by other scientists. I am convinced, currently, that the use of power-sets for biological systems can allow for the reasonable assessment of these systems as irreducibly complex. A power-set is the set of all possible subsets for a given set. If all the parts of a system are known, a power-set of these parts can be made, and this power-set is all possible combinations of parts. This would allow scientists to determine all possibilities for an evolutionary gradation.
To illustrate this, I will be using Behe’s example of the flagellum and apply this method to it. This is a thought experiment, intended to demonstrate how one might use this method, and so I will not be considering all parts of the flagellum. Since I am not trying to argue for the irreducible complexity of the flagellum here, that will not be necessary. If the most basic parts of the flagellum – filament, hook, and basal body – are put into the power-set equation, it looks like this:
- Filament
- Hook
- Basal body
- Filament, hook
- Filament, basal body
- Hook, basal body
- Filament, hook, basal body
In this very simplistic power-set, (7) is the final product, the flagellum; (1-3) are possible first modifications; (4-6) are possible second modifications. If (1-3) could not have evolved by themselves, or if (4-6) could not have evolved by themselves without breaking down the entire system, either being physically impossible or harmful to the organism, then it could be established with reasonable certainty that the flagellum is irreducibly complex. Of course, no accurate assessment could be made from considering these parts alone – all parts of the system would need to be taken into account. I am calling this the “Method for Determining Irreducible Complexity from Biological Power-sets.”
Is it “not 1-3 *and* 4-6 evolve by themselves”, or “not 1-3 *or* 4-6 evolve by themselves”? It seems that if either 1-3 or 4-6 could evolve, then this also entails the other sets could evolve. On the other hand, if 1-3 cannot evolve, then none of the other sets can evolve.
What about partial evolution? E.g. if 1 and 6 can evolve, but none of the others in 1-6. Can 7 still evolve? Or if only 5 cannot evolve, how does that impact 7?
At any rate, this is an interesting approach. The sparser the evolvability of the power set, then the less likely the evolvability of the union. It’d be interesting to quantify thresholds of evolvability affecting the final outcome.
JP,
I think Angus Menuge captured the essential problem of irreducible complexity forcing implausibly large “leaps” between islands of function in dealing with the same basic system, as can be seen from his conditions C1 – 5.
I have summarised:
KF
Isn’t this what biologists already do when they estimate fitness surfaces?
@Bob O’H if it is, then they should be easily able to settle the question of irreducible complexity by demonstrating the powerset is evolvable. It would be quite interesting to see this result.
I wonder if one would also want to consider order as well here (so permutations of parts as opposed to combinations).
Or put a different way, and referring to this diagram showing the power set of {x, y, z}, the set of all paths from the empty set to the full set {x, y, z}.
Edit: I was going to add that we should consider only paths going upward in that diagram (so in the “increasing” direction), but perhaps not. For example, should this path be counted, if the events of x, y, and z arising are not independent?
Empty set -> {x} -> {x, y} -> {y} -> {y, z} -> {x, y, z}
Nice diagram, Dave: 8 possible elements but 12 possible paths. Are there general formulas for n elements?
Hi jdk,
I believe there are 6 “upward” paths here, which is 3!. In general there would be n! upward paths, each one corresponding to a permutation of the features.
If we allow movement downward, then I don’t know the answer—presumably we would want to eliminate those “paths” which repeat the same cycle over and over. (For example x, xy, y, yz, z, xz, x).
jdk,
PS to my #7:
Maybe I understand your post now—there are 12 edges in the graph?
I believe there would be 56 edges in the graph for the power set of {x, y, z, w}.
I think in general the total number of edges for n features would be the sum of (n choose k) * (n choose k + 1) where k ranges from 0 to n – 1. Perhaps there’s a simple formula for that?
With this as the definition, we often set up the problem for defeat. I’ve seen many ‘refutations’ of irreducible complexity. All of them use this one concept: “it is possible”.
Because, that is all that is required.
Trying to show an evolutionist that something is “impossible” – is itself impossible.
What is required to show that the evolution of any imaginable thing is “possible”?
All that is needed is merely an imaginative speculation. If a direct, gradualist pathway to the needed changes seems “unreasonable” (even that is never impossible), then there is gene-sharing, HGT, co-option.
The odds may be 1 in a hundred billion. It’s Dumb and Dumber: “So, you’re telling me there is a chance … Yeah!!!”
It’s never impossible. Of course, if Darwin’s words were taken literally, evolution would have to be “demonstrated” and not just imagined.
But even there, evolutionists can try to “demonstrate” in a lab that a flagellum actually does evolve gradually.
They fail to do this over 30,0000 generations? It’s still not proven “impossible”. We just need to keep waiting.
Michael Behe was a bit naive, I think. He was trusting the good will of his opponents. He trusted their honest judgement. But he received, in reply, all of that dishonesty that claims any kind of evolutionary scenario as being “possible” and therefore IR is supposedly “refuted”.
In any case, I appreciate this approach for precision and I think that evolutionists who are actually honest about the data and possess good will towards their own claims – will indeed be moved to change their views, as many have been.
So I have had good sport flumoxing hard core Darwinists with the IC argument as it applies to a system with scores of billions of almost identical parts, all wired together to act in concert – the respiratory cilia, several per cell. Not a single Darwinian has been able to imagine and explain to me a viable scenario where this system came together gradually like Darwin said himself. You cannot prove that 1% of the celia can work even at a near 1% functional efficiency in the respiratory endothelium. Not even to mention 1% functionality would be a joke of a selective advantage even if it existed. So there you have it – not a single one and do they admit that the Darwinian mechanism is ridiculously unlikely in this, because of their failure? Ridiculously unlikely in itself; they have to have their religion like everyone else, so they come back with stuff like “we’re not going to tell you because you don’t want to learn” or “you’re a d___”.
I should note, at this point, that the flagellum example was just meant as a simplistic way of demonstrating this approach. As I said in the article, it was just an illustration. In reality, Darwinian theorists would never say that a filament appeared, and then a hook, and so on.
A more realistic approach would have to begin with the assumption that all proteins needed are present in other systems. Then if we know all of those proteins, we can make a power-set that could show all possible combinations that might arise by mutation. If there is any point where all possibilities are either harmful or impossible, then it is irreducibly complex.
#9 Silver Asiatic
“evolutionists who are actually honest about the data and possess good will towards their own claims – will indeed be moved to change their views, as many have been.”
Does this relate to the third way folks too?
Jacob Pruse,
Thanks for the article.
kairosfocus
Good point. Thanks.
SA @ 9:
You have spotlighted the selective hyperskepticism in Darwin’s criterion. Something that locks in his RV + NS etc scheme as DEFAULT.
Oops.
Science has no business trafficking with that sort of double-standard on warrant leading to establishing a scheme by default. And you are right that if something sets up, oh if we can make up a just-so story then that is rhetorically good enough, that’s a problem. A big one.
The key issue is again configuration spaces and islands of complex function pivoting on correct and potentially matching parts [just think of laptop plug-in ports!], correctly arranged and coupled to attain function, much as Menuge pointed out with his criteria C1 – 5 which I noted on at 2 above. Once we have that, we have a huge range of possible clumped and scattered at random possibilities which are non-functional, vs a very small fraction of possibilities that would achieve relevant function.
The result is overwhelming needle in haystack blind search challenge that beyond a fairly small threshold of complexity [500 – 1,000 bits of description length by chain of y/n q’s . . . cf. autocad files etc] swamps the atomic and temporal resources of a planet, or of a solar system or of the observed cosmos as a whole. (Beyond that, you leave science and traipse into philosophy as there is no actual observed evidence of a multiverse.)
And yes, I am highlighting that irreducible complexity is a form of functionally specific, complex organisation and/or associated information.
The further point is that IC targets evolutionary systems. Given Menuge’s C1 – 5, the plausibility of proposed mechanisms i/l/o search challenge rapidly falls to zero.
The power set approach sees the config space as a collection, which then turns searches into subsets, from {} to the full space itself. For a space C of cardinality n, the set of subsets — of possible searches — is of cardinality 2^n. For just 500 bits, we have a config space of 3.27*10^150, implying a set of possible searches of 2 ^ [3.27*10^150], i.e. 2^ [2^500].
That’s calculator smoking territory.
In that context search for a golden search becomes search in the power set, obviously exponentially harder than search in the already overwhelming space.
There is no need to posit a blocked path, once there is an utterly implausible one given search challenge.
But of course, if you make a crooked yardstick your standard of reference, you get locked in until things fall utterly apart.
That’s coming.
KF
JP, please note 2 and 15 above. KF
I don’t know why ID’ists are so fixated on the bacterium flagellum when there other, even better, examples of IC. In my opinion, prokaryote DNA replication is a far more daunting problem for the Darwinist. However, instead of one molecular machine, like the flagellum, you have several interacting machines acting in a coordinated manner. This still fits Behe’s definition of IC as being “a single system which is composed of several interacting parts, and where the removal of any one of the parts causes the system to cease functioning.”
For example, to start replication in prokaryote DNA you need an initiation enzyme which creates a replication bubble where another enzyme called helicase attaches itself and begins, like a zipper, to unbind the two complimentary strands of DNA double helix. Another enzyme called primase creates another starting point (a primer) on both of the separated strands known as the 5’ and 3’ or leading and lagging strands. DNA polymerase III uses this primer– actually a short strand of RNA– and adds the complementary nucleobases (A to T, T to A, C to G, G to C) to the single parent strand. In a nutshell, helicase divides one double stranded DNA helix into two single “parent” or template stands to which complimentary nucleotides are added by pol III and the result is two identical double stranded DNA helixes.
Of course, it is somewhat more complicated than that. For example, as helicase unbinds the two strands of the double helix, which are wrapped around each other to begin with, there is a tendency for tangling to occur as a result of the process. Another enzyme called gyrase (or topoisomerase II) is needed to prevent this tangling from occurring. Another problem is that the bases for the lagging strand must added discontinuously which results in short segments know as Okazaki fragments. These fragments must eventually be joined together by an enzyme known as ligase. (We could also discuss error correction which is another part of the replication process.)
Here are a few videos which describe the process in more detail.
https://www.youtube.com/watch?v=O3v04spjnEg&t=2s
https://www.youtube.com/watch?v=bePPQpoVUpM
https://www.youtube.com/watch?v=0Ha9nppnwOc
While it’s true that the flagellum is irreducibly complex it is not essential for life itself. There are a number of single celled organism that exist without flagella. However, life cannot exist without DNA replication (nor transcription, translation etc.) Furthermore, with DNA replication the Darwinist cannot kick the can down the road any further. DNA replication in prokaryotes is as far as you can go and then you are confronted with the proverbial chicken or egg problem. DNA is necessary to create the proteins which are used in its own replication.
The problem with the Darwinian approach is not scientific; it is philosophical. The people committed to this approach believe in it because they believe that natural causes are the ultimate explanation for their existence. However, science has not proven such a world view to be true. So ironically, whatever they believe, they believe it by faith.
Thanks kairosfocus at 2 and 15 and Silver Asiatic at 9. I have found these and other arguments fairly convincing.
However, I have found the following paper to open a little doubt; it claims to undermine irreducible complexity as a barrier in evolution:
– https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4258170/ . Title: “Cryptic Genetic Variation Can Make Irreducible Complexity a Common Mode of Adaptation in Sexual Populations”
The claimed mechanism is that hidden “cryptic genetic variations” are stored as “evolutionary capacitors” and unmasked under environmental and other stresses, to bridge the deep valleys in the fitness landscape that make certain mechanisms irreducibly complex. The paper inherently admits that there are many irreducibly complex biological systems in nature.
From the Introduction: “One mechanism that may allow the evolution of complex adaptations is the revelation of cryptic variation, via a phenomenon known as evolutionary capacitance. When the environment changes and organisms are stressed, evolutionary capacitors switch the status of genetic variation from “off” (phenotypically cryptic) to “on”. After revelation by a capacitor, this previously phenotypically silent genetic variation can acquire fitness consequences, producing a burst of “new” genotypic effects that are potentially adaptive in the new environment. A growing body of both theoretical and laboratory work suggests that such revelation events are a common feature of biological systems.”
Note: It appears that this mechanism would not apply to asexual bacterial IC molecular machines such as the flagellum. This is theoretical only and has not been applied to any actual real world irreducibly complex biological system, with the needed detailed testable step by step model. And this proposed mechanism is perilously similar to the now discredited saltationism and “hopeful monster” hypotheses. Finally, for a real-world biological IC system this proposed mechanism would have to be extended to simultaneously originate the assembly system and its own instructions.
Has this paper ever been addressed by Michael Behe or any of the other ID scientists?
Peter A @ 12
Yes. They see the problems. For example, Stuart Newman sees that references to convergent evolution are ad hoc explanations that simply do not work. So, he promotes an “extended” evolutionary theory. I’d call it “a little less dishonest”, perhaps. Keeping in mind, none of them reject a materialist origins story. They just reject Darwinian gradualism or the RM&NS mechanism.
They attempt to create a new theory but at the same time will not be open to ID as a reasonable alternative.
doubter
This seems to be a new approach to the problem that is cropping up lately. Instead of just having hopeful monsters, they are claiming that organisms develop greater “evolability”. Now that is very convenient because events that are otherwise impossible supposedly can occur because the organism will generate more beneficial mutations when needed.
As I see it, this idea is just another layer built on the assumption that evolution necessarily works. The problem remains: How did this “evolvability” evolve? If an organism is capable of improving its potential to evolve in stressful conditions, this means that evolution is storing potential for a future state.
But that’s just an example of how evolution is claimed to have teleological power – providing purposes to organisms.
KF @ 15
Agreed.
We often think it should be more than sufficient to show that it would take more time than the entire history of the universe to create the information needed to build the complexity in cellular functions in order for an evolutionist to conclude that evolution cannot work.
I notice that Stephen Meyer, for example, has shown that several times and yet that fact is simply resisted.
Darwin’s Black Box was first published in 1996. I do recall when the concept of irreducible complexity was ridiculed. Now, 22 years later a few more admit that it exists.
SA,
It’s been a while since I’ve looked at this, but I don’t recall the existence of irreducible complexity was ever that controversial (see for example stone arches). It’s whether irreducible complexity is diagnostic of intelligent design that is more hotly debated.
daveS
Behe used one example of a mousetrap at the time.
For perhaps 10 years after, his opponents ridiculed that and some claimed that the mousetrap could function without the base (although all they meant was the mechanism could be fixed to the floor instead of on wood). There were many silly arguments like that.
But yes, eventually, Behe’s concept was accepted – although as you said, not the conclusions he drew from it.
Silver Asiatic @ 9,
That’s the gist of their counter argument which is nothing more than naturalistic/materialistic dogmatism, which is rooted in anti-religious bigotry. And, whether or not ID is a religious argument that’s the way they see it and that’s the way they spin it.
Ironically, like most bigoted dogmatists they don’t recognize the irrationality of their thinking. For example, one of the early criticism of Behe’s idea was that it wasn’t falsifiable. However, almost on the heels of that criticism was the argument by the likes of Kenneth Miller and others that IC had been falsified since it was clearly self-evident that the bacterial flagellum could have evolved from the TTSS. (Of course, notice that they didn’t explain how it evolved, simply that it somehow could have evolved from the TTSS.) So what is it? Is IC falsifiable or not? It doesn’t matter to them they’ll just double down on their irrationality.
This is why I think Jacob’s proposal is a little bit misguided. It does no good to repackage the arguments when the critics of ID are not being ethically or intellectually honest. Again, as I said earlier the roots of the conflict are really philosophical not scientific.
JAD
Agreed. That is a blatant example of the dishonesty they use.
It is as if they are saying “in order to accept our theory, you have to be prepared to lie and cover-up your motives”. In other words, use any means you can get away with to defend the idea.
From Dr Behe on falsifying IC as evidence for ID:
and
ET,
If a flagellum did actually appear in this experiment, then an ID proponent could just say the Designer sneaked into the lab and poofed it into existence, couldn’t he?
daves:
Well if it just appeared overnight, yes. But not if it was done as Dr. Behe said.
ET,
Even if the flagellum arose step by step in a gradual process, how would we know the Designer wasn’t responsible?
daves:
Newton’s four rules of scientific reasoning. IOW science 101
ET,
I can see how under Newton’s rules, one would conclude this flagellum arose “naturally” (that is, that’s the preferred explanation), but those rules do not allow one to rule out a divine origin.
daveS
Your straw-man argument maybe unfalsifiable but the design argument is falsifiable as per Behe.
bill cole,
How so?
In order for Behe’s claim to be falsifiable, there would have to be some observation that could refute the claim, in principle.
What observation could demonstrate that the Designer did not deliberately cause some feature such as the flagellum to appear? We don’t have any “Designer-proof” labs; in fact, the Designer is usually held to be omnipresent, at least by ID proponents who post here.
daves:
No, one would conclude it arose artificially. There isn’t anything to suggest any flagellum was produced by nature.
Newton’s rules allow us to differentiate between natural and artificial.
ET,
I was referring to the hypothetical situation where a flagellum arose gradually, step-by-step under laboratory conditions.
I believe you said you would conclude it arose naturally. I would as well, but I don’t believe there is any way to rule out that the Designer did it, so to speak.
daves:
1- If any flagellum arose step-by-step, sequentially, I would infer it was designed to evolve
2- If it arose step-by-step resembling a random walk I would infer materialistic/ stochastic processes did it
3- There needs to be evidence for Designer intervention before one can rule in that possibility